Okay, we are tasked with adding 9095 and 9684. Let's begin!

Step 1: We'll start by adding the digits 5 & 4 in column 1 and get 9.

Step 2: We'll start by adding the digits 9 & 8 in column 2 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 6 in column 3 and get 7.

Step 4: We'll start by adding the digits 9 & 9 in column 4 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

So, 9095 + 9684 = 18779.

